In this paper, a numerical exploration of the perturbed Hill three-body problem under quantum corrections is performed. In particular, the existence of location for the equilibrium points and their stability are explored in both plane and out-of-plane motion of the primaries. The zero velocity curves are found for various values of the Jacobian constant and the different closed or trapped regions in which the infinitesimal body can move are also investigated. We demonstrate that the location and stability of equilibrium points as well as the associated curves of zero velocity are significantly affected by the quantum corrections. Furthermore, the infinitesimal third body can move free around the equilibrium points for decreasing values of the Jacobian constant as the quantized correction parameters increase.

中文翻译：

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量化希尔问题动力学的数值探索

本文对量子修正下的扰动希尔三体问题进行了数值探索。特别是，在初级的平面和平面外运动中探索了平衡点位置的存在及其稳定性。找到了不同雅可比常数值的零速度曲线，并且还研究了无穷小体可以移动的不同封闭或俘获区域。我们证明了平衡点的位置和稳定性以及零速度的相关曲线受到量子修正的显着影响。此外，随着量化校正参数的增加，无穷小的第三体可以围绕雅可比常数值减小的平衡点自由移动。